Fair point. I've updated the animation to address this. The grid now uses the correct non-uniform centroids (optimal for the arcsine distribution in 2D), so you'll see grid lines cluster near the edges where unit-circle coordinates actually concentrate, rather than being evenly spaced. The spacing does change with bit depth.
On the second quantization step: the paper's inner-product variant uses (b-1) bits for the MSE quantizer shown here, then applies a 1-bit QJL (Quantized Johnson-Lindenstrauss) encoding of the residual to make dot-product estimates unbiased. I chose to omit QJL from the animation to keep it digestible as a visual, but I've added a note calling this out explicitly.
On the second quantization step: the paper's inner-product variant uses (b-1) bits for the MSE quantizer shown here, then applies a 1-bit QJL (Quantized Johnson-Lindenstrauss) encoding of the residual to make dot-product estimates unbiased. I chose to omit QJL from the animation to keep it digestible as a visual, but I've added a note calling this out explicitly.